Problem: Simplify the expression. $(3k^{4}-2k^{2}-5k)(-6k^{3}+7k^{2})$
First use the distributive property. $ 3 k^4 (-6 k^3) + 3 k^4 (7 k^2) - 2 k^2 (-6 k^3) - 2 k^2 (7 k^2) - 5 k (-6 k^3) - 5 k (7 k^2) $ Simplify. $ - 18k^{7} + 21k^{6} + 12k^{5} - 14k^{4} + 30k^{4} - 35k^{3} $ $-18k^{7}+21k^{6}+12k^{5}+16k^{4}-35k^{3}$ Identify like terms. $ {- 18k^{7}} {+ 21k^{6}} {+ 12k^{5}} {- 14k^{4}} {+ 30k^{4}} {- 35k^{3}} $ Add the coefficients. $ { -18k^{7}} {+ 21k^{6}} {+ 12k^{5}} {+ 16k^{4}} { -35k^{3}} $